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  title = {Fast deterministic computation of determinants of dense matrices},
  booktitle = {In proceedings of ACM International Symposium on Symbolic
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  year = {1999},
  pages = {1997-2004},
  publisher = {ACM Press}
}

@BOOK{Apostol1997,
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@ARTICLE{ArnoldMonagan2011,
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@ARTICLE{BaiWag1980,
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  number = {152},
  abstract = {We define several types of pseudoprimes with respect to Lucas sequences
	and prove the analogs of various theorems about ordinary pseudoprimes.
	For example, we show that Lucas pseudoprimes are rare and we count
	the Lucas sequences modulo $n$ with respect to which $n$ is a Lucas
	pseudoprime. We suggest some powerful new primality tests which combine
	Lucas pseudoprimes with ordinary pseudoprimes. Since these tests
	require the evaluation of the least number $f(n)$ for which the Jacobi
	symbol $(f(n)/n)$ is less than 1, we evaluate the average order of
	the function $f$.},
  copyright = {Copyright (C) 1980 American Mathematical Society},
  issn = {00255718},
  publisher = {American Mathematical Society},
  url = {http://www.jstor.org/stable/2006406}
}

@ARTICLE{BerTas2010,
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@ARTICLE{BrentKung1978,
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}

@BOOK{Coh1996,
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  year = {1996},
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@BOOK{CraPom2005,
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  edition = {Second},
  month = {August},
}

@ARTICLE{DelegliseNicolasZimmermann2009,
  author   = {Deleglise, Marc and Niclas, Jean-Louis and Zimmermann, Paul},
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  year     = {2009},
  volume   = {20},
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  number   = {3},
  journal  = {Journal de Th\'eorie des Nombres de Bordeaux},
  url      = {http://math.univ-lyon1.fr/~nicolas/dnz4.pdf}
}

@ARTICLE{Dus1999,
  author = {Dusart, Pierre},
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  year = {1999},
  volume = {68},
  pages = {411--415},
  number = {225},
  coden = {MCMPAF},
  doi = {10.1090/S0025-5718-99-01037-6},
  fjournal = {Mathematics of Computation},
  issn = {0025-5718},
  url = {http://dx.doi.org/10.1090/S0025-5718-99-01037-6}
}

@ARTICLE{GowWag2008,
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  title = {Square form factorization},
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  number = {261},
  coden = {MCMPAF},
  doi = {10.1090/S0025-5718-07-02010-8},
  fjournal = {Mathematics of Computation},
  issn = {0025-5718},
  url = {http://dx.doi.org/10.1090/S0025-5718-07-02010-8}
}

@ARTICLE{GraMon1994,
  author = {Granlund, Torbj\"{o}rn and Montgomery, Peter L.},
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  issn = {0362-1340},
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  url = {http://doi.acm.org/10.1145/773473.178249},
  doi = {http://doi.acm.org/10.1145/773473.178249},
  acmid = {178249},
  publisher = {ACM},
  address = {New York, NY, USA},
}

@ARTICLE{GraMol2010,
  author    = {Torbj\"orn Granlund and Niels M\"oller},
  title     = {Improved Division by Invariant Integers},
  journal   = {IEEE Transactions on Computers},
  year      = {2010},
  volume    = {99},
  number    = {PrePrints},
  note      = {draft version available at \url{http://www.lysator.liu.se/~nisse/archive/draft-division-paper.pdf}},
  address   = {Los Alamitos, CA, USA},
  doi       = {http://doi.ieeecomputersociety.org/10.1109/TC.2010.143},
  issn      = {0018-9340},
  publisher = {IEEE Computer Society},
}

@UNPUBLISHED{GouSeb2004,
  author = {Xavier Gourdon and Pascal Sebah},
  title = {The Euler constant: $\gamma$},
  year = {2004},
  note = {\url{http://numbers.computation.free.fr/Constants/Gamma/gamma.html}},
}

@ARTICLE{HaiPap1998,
  author = {Bruno Haible and Thomas Papanikolau},
  title = {Fast multiprecision evaluation of series of rational numbers},
  journal = {Algorithmic Number Theory},
  year = {1998},
  published = {Springer},
}

@UNPUBLISHED{HanZim2004,
  author   = {Guillaume Hanrot and Paul Zimmermann},
  title    = {Newton Iteration Revisited},
  note     = {\url{http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz}},
  year     = {2004},
}

@UNPUBLISHED{Har2009,
  author = {William Hart},
  title  = {A one line factoring algorithm},
  note   = {\url{http://sage.math.washington.edu/home/wbhart/onelinefactor.pdf}},
  year   = {2009},
}

@ARTICLE{Hen1956,
  author   = {Peter Henrici},
  title    = {A Subroutine for Computations with Rational Numbers},
  journal  = {J. ACM},
  year     = {1956},
  volume   = {3},
  pages    = {6--9},
  number   = {1},
  note     = {\url{http://doi.acm.org/10.1145/320815.320818}},
}

@ARTICLE{Hor1972,
  author   = {Ellis Horowitz},
  title    = {Algorithms for Rational Function Arithmetic Operations},
  journal  = {Annual ACM Symposium on Theory of Computing:  Proceedings of the Fourth Annual ACM Symposium on Theory of Computing (Denver)},
  year     = {1972},
  pages    = {108--118},
  note     = {\url{http://doi.acm.org/10.1145/800152.804903}},
}

@BOOK{Knu1997,
  author    = {Donald Knuth}, 
  title     = {The Art of Computer Programming Vol.~2, Seminumerical Algorithms}, 
  edition   = {third}, 
  publisher = {Addison--Wesley}, 
  address   = {Reading, Massachusetts},
  year      = {1997},
}

@ARTICLE{Knuth1977,
  author = {Donald Knuth},
  title = {Notes on Generalized Dedekind Sums},
  journal = {Acta Arithmetica},
  year = {1977},
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  pages = {297--325},
}

@ARTICLE{LukPatWil1996,
  author   = {Lukes, R. F. and Patterson, C. D. and Williams, H. C.},
  title    = {Some results on pseudosquares},
  journal  = {Math. Comp.},
  year     = {1996},
  volume   = {65},
  pages    = {361--372, S25--S27},
  number   = {213},
  note     = {available at \url{http://www.ams.org/journals/mcom/1996-65-213/S0025-5718-96-00678-3/S0025-5718-96-00678-3.pdf}},
  coden    = {MCMPAF},
  doi      = {10.1090/S0025-5718-96-00678-3},
  fjournal = {Mathematics of Computation},
  issn     = {0025-5718},
  url      = {http://dx.doi.org/10.1090/S0025-5718-96-00678-3}
}

@ARTICLE{MasRob1996,
  author   = {Massias, Jean-Pierre and Robin, Guy},
  title    = {Bornes effectives pour certaines fonctions concernant les nombres
	premiers},
  journal  = {J. Th\'eor. Nombres Bordeaux},
  year     = {1996},
  volume   = {8},
  pages    = {215--242},
  number   = {1},
  fjournal = {Journal de Th\'eorie des Nombres de Bordeaux},
  issn     = {1246-7405},
  url      = {http://jtnb.cedram.org/item?id=JTNB_1996__8_1_215_0}
}

@ARTICLE{Mul2000,
  author  = {Thom Mulders},
  title   = {On Short Multiplications and Divisions},
  journal = {AAECC},
  year    = {2000},
  volume  = {11},
  pages   = {69--88}
}

@ARTICLE{NakTurWil1997,
  author  = {Nakos, George and Turner, Peter and Williams, Robert},
  title   = {Fraction-free algorithms for linear and polynomial equations},
  journal = {ACM SIGSAM Bull.},
  year    = {1997},
  volume  = {31},
  number  = {3},
  pages   = {11--19},
}

@ARTICLE{Rademacher1937,
  author = {Rademacher, Hans},
  title = {On the partition function $p(n)$},
  journal = {Proc. London Math. Soc},
  volume = {43},
  year = {1937},
  pages = {241--254}
}

@ARTICLE{RosSch1962,
  author   = {Rosser, J. Barkley and Schoenfeld, Lowell},
  title    = {Approximate formulas for some functions of prime numbers},
  journal  = {Illinois J. Math.},
  year     = {1962},
  volume   = {6},
  pages    = {64--94},
  fjournal = {Illinois Journal of Mathematics},
  issn     = {0019-2082},
}

@ARTICLE{ThullYap1990,
    author = {Thull, K. and Yap, C.},
    title  = {A Unified Approach to {HGCD} Algorithms for Polynomials and Integers},
    year   = {1990}
}

@ARTICLE{Zei1995,
  author  = {D.~Zeilberger}, 
  title   = {The {J}.{C}.{P}.~{M}iller Recurrence for Exponentiating a Polynomial, 
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  journal = {Journal of Difference Equations and Applications},
  year    = {1995}, 
  volume  = {1}, 
  pages   = {57--60},
}

@ARTICLE{WaktinsZeitlin1993,
  author = {Watkins, W. and Zeitlin, J.},
  title = {The minimal polynomial of $\cos(2\pi/n)$},
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  volume = {100},
  number = {5},
  year = {1993},
  pages = {471--474},
}

@ARTICLE{Whiteman1956,
  author = {Whiteman, A. L.},
  title = {A sum connected with the series for the partition function},
  journal = {Pacific Journal of Mathematics},
  year = {1956},
  volume = {6},
  number = {1},
  pages = {159--176},
}

